Question: Rewrite as a simplified fraction. ${1.\overline{89} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 189.8989...\\ 1x &= 1.8989...\end{align*}}$ Subtracting the two equations, we have: ${99x = 188}$ ${x = \dfrac{188}{99}} \text{or} {1 \dfrac{89}{99}}$